This is the model of your battery Asus A6000U -
Compatible Replacement Li-ion battery. 14.8V 4800mAh. Equivalent to A42-A3, 90-NA51B2000, 90-NA52B2000, 70-NDK1B2001 -- CBI0967A
regarding for removal-you can see at the backside of the LCD,you can remove by pressing the lock to unlock.

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This is not a computer problem, but rather a problem of the game setup.
Start your game and go to "setup" or "options" or something like that. One of the options will be related to "mouse speed" or "mouse sensitivity". Turn the speed or sensitivity down a couple of notches, save the new settings and try the game again.

Keyboards are most generally held by screws in one of two places. 1- On the bottom, could be marked with a K, With bottom screws, the keyboard may have tabs on it holding it, you will need to pry the tabs gently out away from the plastics. 2- towards the top of the keyboard under the power button strip. Try this link, you may be able to find a breakdown diagram for your machine there.http://repair4laptop.org/notebook.html

Don't be afraid to remove all the screws on the bottom of the machine if you're unsure as to which are for the keyboard, it won't hurt anything as long as you get them all back in. If they're marked with a B, it's a motherboard screw, and P is for plastic casing.